Computer assisted optics teaching at the Moscow Institute ofPhysics and Technology

N.N.Soboleva, S.M.Kozel, G.R.Lockshin, MA. Entin, K.V. Galichsky,P.L. Lebedinsky, P.M. Zhdanovich

Moscow Institute ofPhysics and Technology

ABSTRACT

Traditional methods used in optics teaching lack clarity and vividness when illustrating abstractnotions such as polarization or interference. Here's where computer models may help, but they usuallyshow only a single phenomenon or process and don't let the student see the entire picture. For thisreason at Moscow Institute of Physics and Technology was developed the courseware "Wave Opticson the Computer' consisting of a number of related simulations. It is intended for students studyingoptics at the Universities. Recently we have developed different simulations in optics for secondaryschool level. They are included as part oflarge computer courseware "PHYSICS by PICTURES".

The courseware "Wave Optics on the Computer" consists of nine large simulation programs andthe textbook. The programs are simulating basic phenomena of wave optics. Parameters of opticalsystems can be varied by the user. The textbook contains theoretical considerations on studied opticalphenomena, recommendations concerning work with computer programs, and, especially for thosewishing to deeper understand wave optics, original problems for individual solution.

At the Moscow Institute of Physics and Technology the course "Wave Optics on the Computer"is used for teaching optics in the course of general physics. The course provides both computerassisted teaching for lectures support and computer assisted learning for students during a seminars inthe computer classroom.

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1.1. Interference

1. WAVE OPTICS

This program is designed to illustrate the ftmdamental laws of light wave interference. Variousdouble-beam optical interference systems are simulated, i.e. Young's experiment, Fresnel bimirror,Michelson interferometer, interference in plane-parallel plate, Lloyd's mirror, Michelson stellarinterferometer. The possibility of varying parameters of interference systems and the incident lightwavelength is provided. Using Young's experiment as an example, the interference of partiallycoherent waves is simulated. The influence of light coherency properties and finite size of the sourceson the interference pattern is studied.

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1.2. Diffraction

This program simulates diffraction of light waves on holes of different shape (round holes andslits). Both diffraction in the near zone (Fresnel diffraction) and far zone (Fraunhoffer diffraction) iscovered by the program. Spatial distribution of light intensity in diffraction phenomena is simulatedand displayed on the screen. Parameters of the model can be varied.

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Intensity distribution

1.3. Diffraction grating

This program simulates the operating of diffraction grating. While various parameters of themodel (such as wave length, period and number of slits, etc.) can be varied by the user the programcalculates angular dispersion, dispersion range, resolution power etc, and presents the results in vividpictures to be easily understood and remembered by students.

1.4. Optical instruments

This program illustrates chief principles of work of simple optical instruments. Main attention ispaid to the influence of diffraction phenomena on the optical instrument operation. The work of humaneye, lens, microscope and telescope is simulated. There is the possibility to change geometricalparameters of the devices and observe the results.

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1.5. Polarization

This program demonstrates some properties of elliptically polarized light. Optical constructorcontained in this program enables one to study operation of polarizing plates and double refractingplates. The program provides possibility to vary characteristics of input light and observe change ofproperties of output light beam.

The program demonstrates phase and group velocities of light waves. Differences between phaseand group velocities are explained on the example of superposition of three waves. Amplitudes andfrequencies of these three waves can be varied in the program. Propagation of various wave packets issimulated in substances with different dispersion laws. Observation of normal and abnormal dispersionsis provided. In some cases decay of wave packets can be observed.

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ELLIPTICAL POLARIZATION

Phase

1.6. Wave packets

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2. ELEMENTS OF FOURIER OPTICS

2.1 Fourier analysis

This program strives at explaining basic concepts of the theory of spectral expansions, such asdirect and inverse Fourier transforms of some classes of periodical and aperiodic functions, discreteand continuous spectra, physical sense of positive and negative frequencies. The program allows forthe parameters of studied functions to be varied. For periodic functions the program provides thepossibility to observe single harmonic components and synthesize the former function with the help ofinverse Fourier transform. For aperiodic functions the program allows to observe widening of spectraresulting from shortening of process duration and hence to clarify the uncertainty principle which isvery important in physics of waves and vibrations. This program may be regarded as theoreticalintroduction to Fourier optics. It can be used as a separate program for education in vibrationalphenomena, in electric circuits, mechanical systems etc.

2.2. Fourier optics

This program illustrates general ideas of Fourier optics on the bases of simulation of variousoptical problems, such as plane wave expansion of optical field, diffraction of light on varioustransparences, on amplitude and phase sinusoidal gratings, phenomenon of self-reproduction of light,principle of double diffraction, spatial filtration and multiplication of optical images.

2.3. Two-dimensional Fourier transform

This program provides the possibility to investigate spatial Fourier transform on the bases ofCatron optical system. Fast Fourier Transform algorithm is used in calculations. The program allowsfor different optical transparencies to be chosen from the predefined set of pictures as well as newtransparencies of arbitrary shape to be drawn by the user. After choice of the object the programcarries out two-dimensional Fourier transform and builds up Fourier image as two-dimensional pictureon display screen. Possibility of different manipulations with Fourier image is provided, such asmasking of image with diaphragms and gratings, addition and subtraction of images etc. Afler editingFourier image the program allows one to carry out second Fourier transform to get optical image andcompare it with the original object.

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IIHPT

PHYSICS by PICTURES is educational computer courseware for both teachers andschoolchildren. It consists of reference book and a set of computer simulations from Mechanics,Thermodynamics and Molecular Physics, Electricity and Magnetizm, Optics, Quantum Physics as wellas Historical Experiments examples. Some questions and different problems are included withpossibility to enter answer and check it.

3.1. Light and shadow

There is visualized creation of shade and half-shade from the object and geometric light beamsmotion. It is possible to change size and position of the source, size and position of the obstacle.

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3. PHYSICS BY PICTURES, PART "OPTICS"

3.2. Refraction and reflection of rays

There is studied the law of light reflection from plane mirror. It is possible to change rayincidence angle and mirror angles. There are also studied laws of light refraction and reflection on theinterface between air and glass in the computer experiment. It is possible to change ray incidenceangle, glass refractive index, measure reflection and refraction angles. The phenomenon of totalinternal reflection on the interface between glass and air is studied.

3.3. Thin lens

The program demonstrates collecting and diverging lenses with different optical strength. It ispossible to observe rays motion from remote source and look through the concept of focal point, focallength and optical strength of the thin lens. It is also possible to study the dependence between focallength of thin spherical lens and curvature of its surfaces and refractive indices of the lens andsurrounding medium.

3.4. Lens as an optical tool

The simulation makes it possible to get images of objects in computer experiment with the aid ofcollecting and diverging lenses. It is also possible to choose the type of the lens and its focal length, tochange object position and determine linear magnification.

3.5. Optical constructor

The program allows to construct image of object in optic system consisting of two lenses. It ispossible to change object position, kind and parameters of lenses and the distance between them todetermine linear magnification of two lens system. The program demonstrates rays motion in opticaldevices (microscope and telescope).

3.6. Spherical mirror

The program illustrates constructing the image of an object in concave and convex sphericalmirrors. The concepts of focus and focal length of spherical mirror are studied. It is possible to changeobject position relative to the mirror, kind of the mirror and its curvature radius as well as determinelinear magnification of image.

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3.7. Eye as an optical tool

There is studied motion of rays in an eye and position of image relative to retina depending onposition of the object. It is possible to choose type of the eye -normal, near-sighted, far-sighted, lookthrough the phenomenon of eye accomodation. Rays motion is presented for three different cases: eyeis accomodated on the farthest accomodation point, eye is accomodated on the distant of normalvision, eye automatically changes its optical strength for the image of the object to remain on retinaindependently of position of the object. It is also possible to look through glasses operation.

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3.8. Interference

There is studied the phenomenon of interference on the example of Young's experiment. It ispossible to observe interference fringes on the screen, plot of light intensity distribution and determinewidth of interference fridges. The simulation provides possibility of changing light wave length,distance between splits in Young's scheme and studing the influence of these parameters oninterference pattern.

3.9. Grating as an optical tool

There is studied intensity distribution in diffraction pattern received from lattice with differentnumber of splits. It is possible to observe rays motion, generate different orders of diffraction. Theprogram allows to change number of splits in diffraction grating, its period and incident light wavelength. Using the light consisting of two spectral lines it is possible to ensure that diffraction gratingresolves them.

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3.10. Diffraction in lens focus

There is observed image of the remote point source in the lens focus which is blurred because oflight diffraction on lens aperture (on entrance hole). It is possible to change focal length, diameter ofentrance aperture and light wave length.

3.11. Fresnel zones

The program allows to observe diffraction patterns from light diffraction on round apertures andround disks. It is possible to construct different zone plates, close or open any of first six ring Fresnelzones.

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3.12. Light polarization

There is studied the phenomenon of light polarization with the aid of optical scheme consistingof light source, two polarizers and the screen. It is possible to change the orientation of permitteddirections of polarizers, illustrate Malus law for the light consisting of different spectral components.

3.13. Light speed. Michelson experiment

The program demonstrates Michelson's experiment measuring the speed of light. It is possible todetermine the speed of light changing angular velocity of octahedral mirror.

3.14. Light dispersion

The simulation allows to carry out computer experiment analogous to that of Newton's onresolution of white light in spectrum with the aid of a prism. It is possible to observe deviation ofmonochromatic light beams with different wave lengths by prism. The phenomenon of dispersion isalso studied.

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